arXiv subjects

Francesco Ghisoni

Publications and source records attributed to Francesco Ghisoni.

5 recordsLinked to original sources

arXiv2026

Efficient Complex-Valued State Preparation on Bucket Brigade QRAM

Efficient quantum state preparation is a critical component in quantum algorithms that process large classical data, and it is fundamental to realizing quantum advantage in domains such as machine learning, quantum linear algebra, and quantum finance. Building on the framework of~\cite{berti2025efficient}, which integrates Bucket Brigade QRAM (BBQRAM) with a segment tree to achieve amplitude encoding in polylogarithmic query time, we present two improvements within the same architecture-aware framework. First, we remove the $U_{2\mathrm{CR}}$ subroutine by classically precomputing the rotation angles determined by the segment tree and storing these angles directly in the BBQRAM cells. The tradeoff is that the classically loaded QRAM stores precomputed fixed-point angles rather than raw subtree weights. Second, we extend the construction to complex-valued matrices $A \in \mathbb{C}^{M \times N}$ by storing a leaf phase alongside each precomputed rotation angle and using a two-step magnitude-then-phase procedure; the real signed case is naturally subsumed as a one-bit phase specialization. At unchanged $\mathcal{O}(\log_2^2(MN))$ BBQRAM query complexity, the QPU procedure reduces to BBQRAM retrievals and controlled-rotation cascades, with $\mathcal{O}(MN)$ memory cells per matrix and no reversible arithmetic on the QPU.

quant-ph↗

arXiv2025

Spectral Gap Estimation via Adiabatic Preparation

Estimating energy gaps, i.e. the energy difference between two different states, in quantum systems is crucial for understanding their properties. Conventionally, spectral gap estimation relies on independently computing the ground-state and first-excited-state energies and then taking their difference. This work introduces an alternative procedure for estimating spectral gaps on digital quantum devices using the Adiabatic Preparation technique to create a specific superposition state. The expectation values of observables measured on such a state exhibit time-dependent fluctuations which, through a fitting process, can be used to estimate the energy gap. We successfully test our method on the 1D and 2D Ising models, and H2 and He2 molecules, implementing relatively shallow circuits both on noiseless and noisy simulators. The robustness of the approach is corroborated by additional experiments on the real IonQ Aria device for the 1D Ising model up to 20 qubits, demonstrating the applicability of the proposed method for currently available digital quantum devices and paving the way for more complex energy gap calculation requiring deeper circuits in the fault-tolerant era to come.

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arXiv2025

Efficient Quantum State Preparation with Bucket Brigade QRAM

The preparation of data in quantum states is a critical component in the design of quantum algorithms. The cost of this step can significantly limit the realization of quantum advantage in domains such as machine learning, finance, and chemistry. One of the main approaches to achieve efficient state preparation is through the use of Quantum Random Access Memory (QRAM), a theoretical device for coherent data access with several proposed hardware implementations. In this work, we present a framework that integrates the hardware model of the Bucket Brigade QRAM (BBQRAM) with the classical data structure of the Segment Tree to achieve efficient state preparation. We introduce a memory layout that embeds a segment tree within BBQRAM memory cells by preserving the segment tree's hierarchy and supporting data retrieval in logarithmic time via specialized access primitives. We demonstrate that our method encodes a matrix $A \in \mathbb{R}^{M \times N}$ in a quantum register of $\Theta(\log_2(MN))$ qubits in $\mathcal{O}(\log_2^2(MN))$ time, {requiring a constant number of working qubits (under fixed precision) and $\mathcal{O}(MN)$ memory cells within the BBQRAM architecture.} We further illustrate the method through a numerical example. This framework provides theoretical support for quantum algorithms that assume negligible data loading overhead and establishes a foundation for designing classical-to-quantum encoding algorithms that are aware of the underlying hardware QRAM architecture.

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arXiv2024

Resource-efficient quantum algorithm for linear systems of equations

Finding the solution to linear systems is at the heart of many applications in science and technology. Over the years a number of algorithms have been proposed to solve this problem on a digital quantum device, yet most of these are too demanding to be applied to the current noisy hardware. In this work, an original algorithmic procedure to solve the Quantum Linear System Problem (QLSP) is presented, which combines ideas from Variational Quantum Algorithms (VQA) and the framework of classical shadows. The result is the Shadow Quantum Linear Solver (SQLS), a quantum algorithm solving the QLSP avoiding the need for large controlled unitaries, requiring a number of qubits that is logarithmic in the system size. In particular, our heuristics show an exponential advantage of the SQLS in circuit execution per cost function evaluation when compared to other notorious variational approaches to solving linear systems of equations. We test the convergence of the SQLS on a number of linear systems, and results highlight how the theoretical bounds on the number of resources used by the SQLS are conservative. Finally, we apply this algorithm to a physical problem of practical relevance, by leveraging decomposition theorems from linear algebra to solve the discretized Laplace Equation in a 2D grid for the first time using a hybrid quantum algorithm.

quant-ph↗

arXiv2024

Spectral Gap Superposition States

This work introduces a novel NISQ-friendly procedure for estimating spectral gaps in quantum systems. By leveraging Adiabatic Thermalization, we are able to create the Spectral Gap Superposition state, a newly defined quantum state exhibiting observable fluctuations in time that allow for the accurate estimation of any energy gap. Our method is tested by estimating the energy gap between the ground and the first excited state for the 1D and 2D Ising model, the Hydrogen molecule H2 and Helium molecule He2. Despite limiting our circuit design to have at most 40 Trotter steps, our numerical experiments of both noiseless and noisy devices for the presented systems give relative errors in the order of $10^{-2}$ and $10^{-1}$. Further experiments on the IonQ Aria device lead to spectral gap estimations with a relative error of $10^{-2}$ for a 4-site Ising chain, demonstrating the validity of the procedure for NISQ devices and charting a path towards a new way of calculating energy gaps.

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